%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET687+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n023.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 00:21:25 EDT 2022 % Result : Theorem 3.14s 1.41s % Output : Proof 4.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SET687+4 : TPTP v8.1.0. Released v2.2.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n023.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jul 10 13:27:40 EDT 2022 % 0.12/0.33 % CPUTime : % 0.50/0.61 ____ _ % 0.50/0.61 ___ / __ \_____(_)___ ________ __________ % 0.50/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.50/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.50/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.50/0.61 % 0.50/0.61 A Theorem Prover for First-Order Logic % 0.50/0.62 (ePrincess v.1.0) % 0.50/0.62 % 0.50/0.62 (c) Philipp Rümmer, 2009-2015 % 0.50/0.62 (c) Peter Backeman, 2014-2015 % 0.50/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.50/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.50/0.62 Bug reports to peter@backeman.se % 0.50/0.62 % 0.50/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.50/0.62 % 0.50/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.82/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.39/0.92 Prover 0: Preprocessing ... % 2.05/1.11 Prover 0: Warning: ignoring some quantifiers % 2.05/1.13 Prover 0: Constructing countermodel ... % 2.51/1.25 Prover 0: gave up % 2.51/1.25 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.64/1.27 Prover 1: Preprocessing ... % 3.14/1.39 Prover 1: Constructing countermodel ... % 3.14/1.41 Prover 1: proved (158ms) % 3.14/1.41 % 3.14/1.41 No countermodel exists, formula is valid % 3.14/1.41 % SZS status Theorem for theBenchmark % 3.14/1.41 % 3.14/1.41 Generating proof ... found it (size 11) % 3.94/1.62 % 3.94/1.62 % SZS output start Proof for theBenchmark % 3.94/1.62 Assumed formulas after preprocessing and simplification: % 3.94/1.62 | (0) ? [v0] : ? [v1] : ( ~ (v1 = 0) & subset(v0, v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (product(v3) = v4) | ~ (member(v2, v5) = v6) | ~ (member(v2, v4) = 0) | ? [v7] : ( ~ (v7 = 0) & member(v5, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (difference(v4, v3) = v5) | ~ (member(v2, v5) = v6) | ? [v7] : ? [v8] : (member(v2, v4) = v7 & member(v2, v3) = v8 & ( ~ (v7 = 0) | v8 = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (union(v3, v4) = v5) | ~ (member(v2, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & ~ (v7 = 0) & member(v2, v4) = v8 & member(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (intersection(v3, v4) = v5) | ~ (member(v2, v5) = v6) | ? [v7] : ? [v8] : (member(v2, v4) = v8 & member(v2, v3) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (sum(v3) = v4) | ~ (member(v2, v6) = 0) | ~ (member(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & member(v6, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (product(v3) = v4) | ~ (member(v2, v4) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & member(v6, v3) = 0 & member(v2, v6) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (unordered_pair(v3, v2) = v4) | ~ (member(v2, v4) = v5)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (unordered_pair(v2, v3) = v4) | ~ (member(v2, v4) = v5)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (power_set(v3) = v4) | ~ (member(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v2, v3) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v2 | v3 = v2 | ~ (unordered_pair(v3, v4) = v5) | ~ (member(v2, v5) = 0)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (unordered_pair(v5, v4) = v3) | ~ (unordered_pair(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (difference(v5, v4) = v3) | ~ (difference(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (union(v5, v4) = v3) | ~ (union(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (intersection(v5, v4) = v3) | ~ (intersection(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (equal_set(v5, v4) = v3) | ~ (equal_set(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (subset(v5, v4) = v3) | ~ (subset(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (member(v5, v4) = v3) | ~ (member(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (difference(v4, v3) = v5) | ~ (member(v2, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & member(v2, v4) = 0 & member(v2, v3) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (union(v3, v4) = v5) | ~ (member(v2, v5) = 0) | ? [v6] : ? [v7] : (member(v2, v4) = v7 & member(v2, v3) = v6 & (v7 = 0 | v6 = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection(v3, v4) = v5) | ~ (member(v2, v5) = 0) | (member(v2, v4) = 0 & member(v2, v3) = 0)) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (singleton(v2) = v3) | ~ (member(v2, v3) = v4)) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (equal_set(v2, v3) = v4) | ? [v5] : ? [v6] : (subset(v3, v2) = v6 & subset(v2, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & member(v5, v3) = v6 & member(v5, v2) = 0)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (product(v4) = v3) | ~ (product(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (sum(v4) = v3) | ~ (sum(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (singleton(v4) = v3) | ~ (singleton(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (singleton(v3) = v4) | ~ (member(v2, v4) = 0)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (power_set(v4) = v3) | ~ (power_set(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sum(v3) = v4) | ~ (member(v2, v4) = 0) | ? [v5] : (member(v5, v3) = 0 & member(v2, v5) = 0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (power_set(v3) = v4) | ~ (member(v2, v4) = 0) | subset(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : ( ~ (subset(v2, v3) = 0) | ~ (member(v4, v2) = 0) | member(v4, v3) = 0) & ! [v2] : ! [v3] : ( ~ (equal_set(v2, v3) = 0) | (subset(v3, v2) = 0 & subset(v2, v3) = 0)) & ! [v2] : ~ (member(v2, empty_set) = 0)) % 4.23/1.67 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 4.23/1.67 | (1) ~ (all_0_0_0 = 0) & subset(all_0_1_1, all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0) % 4.37/1.69 | % 4.37/1.69 | Applying alpha-rule on (1) yields: % 4.37/1.69 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 4.37/1.69 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 4.37/1.69 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 4.37/1.69 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 4.37/1.69 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) % 4.37/1.69 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 4.37/1.69 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 4.37/1.69 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 4.37/1.69 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 4.37/1.69 | (11) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 4.37/1.69 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 4.37/1.69 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 4.37/1.70 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) % 4.37/1.70 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) % 4.37/1.70 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 4.37/1.70 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 4.37/1.70 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 4.37/1.70 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.37/1.70 | (20) subset(all_0_1_1, all_0_1_1) = all_0_0_0 % 4.37/1.70 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) % 4.37/1.70 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 4.37/1.70 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 4.37/1.70 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 4.37/1.70 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 4.37/1.70 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 4.37/1.70 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) % 4.37/1.70 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 4.37/1.71 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 4.37/1.71 | (30) ~ (all_0_0_0 = 0) % 4.37/1.71 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 4.37/1.71 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 4.37/1.71 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 4.37/1.71 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 4.37/1.71 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 4.37/1.71 | (36) ! [v0] : ~ (member(v0, empty_set) = 0) % 4.37/1.71 | % 4.37/1.71 | Instantiating formula (28) with all_0_0_0, all_0_1_1, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_1_1) = all_0_0_0, yields: % 4.37/1.71 | (37) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_1_1) = 0) % 4.37/1.71 | % 4.37/1.71 +-Applying beta-rule and splitting (37), into two cases. % 4.37/1.71 |-Branch one: % 4.37/1.71 | (38) all_0_0_0 = 0 % 4.37/1.71 | % 4.37/1.71 | Equations (38) can reduce 30 to: % 4.37/1.71 | (39) $false % 4.37/1.71 | % 4.37/1.71 |-The branch is then unsatisfiable % 4.37/1.71 |-Branch two: % 4.37/1.71 | (30) ~ (all_0_0_0 = 0) % 4.37/1.71 | (41) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_1_1) = 0) % 4.37/1.71 | % 4.37/1.71 | Instantiating (41) with all_10_0_2, all_10_1_3 yields: % 4.37/1.71 | (42) ~ (all_10_0_2 = 0) & member(all_10_1_3, all_0_1_1) = all_10_0_2 & member(all_10_1_3, all_0_1_1) = 0 % 4.37/1.71 | % 4.37/1.71 | Applying alpha-rule on (42) yields: % 4.37/1.71 | (43) ~ (all_10_0_2 = 0) % 4.37/1.71 | (44) member(all_10_1_3, all_0_1_1) = all_10_0_2 % 4.37/1.71 | (45) member(all_10_1_3, all_0_1_1) = 0 % 4.37/1.71 | % 4.37/1.71 | Instantiating formula (26) with all_10_1_3, all_0_1_1, 0, all_10_0_2 and discharging atoms member(all_10_1_3, all_0_1_1) = all_10_0_2, member(all_10_1_3, all_0_1_1) = 0, yields: % 4.37/1.71 | (46) all_10_0_2 = 0 % 4.37/1.71 | % 4.37/1.71 | Equations (46) can reduce 43 to: % 4.37/1.71 | (39) $false % 4.37/1.71 | % 4.37/1.71 |-The branch is then unsatisfiable % 4.37/1.71 % SZS output end Proof for theBenchmark % 4.37/1.71 % 4.37/1.71 1082ms %------------------------------------------------------------------------------